$$ What effects does changing the modulated frequency have on the spectral density? $(5$ points$)$

Changing the modulating frequency shifts the centre frequency of the spectral density. The spectral peaks will appear around the modulating frequency and its harmonics, with higher modulating frequencies pushing the peaks further apart in the frequency domain. This change is due to the relationship between the carrier and modulating signal frequencies, which defines the spacing of spectral components in amplitude modulation.

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$$ Why does the spectrum have a comb structure and what is the spectral distance between impulses? Why? $(5$ points$)$

The comb structure in the spectrum arises because of the periodic modulation of the triangular pulse. Each spectral impulse corresponds to a harmonic of the modulation frequency. The spectral distance between impulses is equal to the modulating frequency itself because this frequency determines the rate at which the carrier signal is modulated, resulting in regularly spaced frequency components in the spectrum.

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$$ What would happen to the spectral density if the period of the triangle pulse were to increase toward infinity? $($In the limit$)(5$ points$)$

As the period of the triangular pulse increases toward infinity, the modulation rate decreases, which compresses the spectral impulses closer together. In the limit$,$ as the period approaches infinity, the modulation becomes a DC $($constant$)$ signal, and the comb structure would collapse into a single spectral line at the carrier frequency, with no additional sidebands. This is because a longer period means lower frequency modulation, reducing the spectral spread.